a broadband/resonant search for axion dark...

A Broadband/Resonant Search for Axion Dark Matter

Jonathan OuelletOctober 30, 2018Massachusetts Institute of Technology

Massachusetts Institute of Technology, LNS Special Seminar, October 30, 2018

The Case For Dark Matter

The Case for Dark Matter

There is extensive evidence for the presence of Dark Matter in the Universe

▸ Galactic rotation curves

▸ Measurements of the CMB

▸ Weak Lensing, Clustering and Galactic dynamics (e.g. Bullet cluster)

2

The Standard Model

What we don’t understand


The Case For Dark Matter

So What Is Dark Matter?

▸ We know that it requires physics beyond the Standard Model!

▸ Interacts gravitationally.

▸ Does it interact Weakly? EM? New force mediator that mixes with the SM?

▸ 70 orders of magnitude in viable mass range

3

➡ Favor theories that solve more than one problem at once!

Figure from T. Tait

AXION DARK MATTER

THE CASE FOR


Strong CP-Problem

The Wonky Table of QCD Physics

▸ The most general interaction that you can write down for the QCD interaction contains a CP-violating term

▸ Θ is arbitrary in the range: 0 ≤ Θ ≤ 2π

‣ The strong interaction should violate CP … a lot!

▸ Current limits on the neutron EDM place

➡ This is the Strong CP Problem!

⇥ ⌘ ⇥+ arg (det (M 0))

5

L � �↵s

8⇡Ga

µ⌫Gaµ⌫ � ⇥

↵s

8⇡Ga

µ⌫eGaµ⌫

��⇥�� < 10�10


Strong CP-Problem

The Wonky Pool Table

6

θ~?∘

Analogy from Pierre Sikivie


Strong CP-Problem


6

θ~?∘

θ<10-10∘



Strong CP-Problem

Peccei-Quinn Mechanism

▸ Introduce a new field with the same CP violating term

▸ Interactions with SM (QCD) give the field a potential which cause it to:

▸ dynamically cancel Θ!

▸ gain a small but non-zero mass:

7

ma ⇠ m⇡f⇡fa

⇠ 10�9 eV

✓1016 GeV

fa

◆

afa

Θ

/ cos

✓a

fa� ⇥

◆

L � �↵s

8⇡Ga

µ⌫Gaµ⌫ +

✓a

fa� ⇥

◆↵s

8⇡Ga

µ⌫Gaµ⌫


Strong CP-Problem


8

θ~?∘



Axion Dark Matter

Axion Dark Matter

9

• Misalignment mechanism gives rise to an oscillating axion field:

• The combined field potential/kinetic energy behaves like DM!

• We can write the present day energy density in terms of the mass and initial alignment angle:

afa

Θ

⇥i

a(t) = a0 sin(mat)

⌦ah2 ⇠ 0.1

✓10�5 eV

ma

◆7/6

⇥2i

DETECTING AXION DARK MATTER


Detecting Axion Dark Matter

Particle vs Field

WIMPs behave like a dilute gas of particles zipping around. Occasionally one might bump into our detector.

A few WIMPs per liter of space.

11



Particle vs Field

WIMPs behave like a dilute gas of particles zipping around. Occasionally one might bump into our detector.

A few WIMPs per liter of space.

11

Axions have a much higher number density and so behave like a classical field. Creating a very weak oscillating “wind” that we search for.

~1018 axions per liter of space



Axion Interactions with the Standard Model

▸ In addition to canceling the CP violating term, the axion also adds a lot of interactions with the SM!

12

L = LSM +

✓a

fa� ⇥

◆↵s

8⇡Ga

µ⌫eGaµ⌫

�1

2@µa@

µa+ Lint(a/fa, SM)

La�� = �1

4ga��aFµ⌫

eFµ⌫

= �ga��aE ·B

ga�� ⇠ ↵

2⇡fa⇠ 1.2⇥ 10�19 GeV�1

⇣ ma

10�9 eV

⌘ga�� / ↵EM

fa




▸ New QED Lagrangian leads to new Maxwell’s equations

13

L = �1

4Fµ⌫F

µ⌫ � 1

4ga��aF

µ⌫ eFµ⌫

r ·E = �ga��B ·ra

r ·B = 0

r⇥E = �@B

@t

r⇥B =@E

@t� ga��

✓E⇥ra� @a

@tB

◆

Modified Source-Free Maxwell’s Equations





13

L = �1

4Fµ⌫F

µ⌫ � 1

4ga��aF

µ⌫ eFµ⌫


r ·B = 0

r⇥E = �@B

@t

r⇥B =@E

@t� ga��

✓E⇥ra� @a

@tB

◆

Modified Source-Free Maxwell’s Equations≈0

≈0





13

L = �1

4Fµ⌫F

µ⌫ � 1

4ga��aF

µ⌫ eFµ⌫


r ·B = 0

r⇥E = �@B

@t

r⇥B =@E

@t� ga��

✓E⇥ra� @a

@tB

◆

Modified Source-Free Maxwell’s Equations≈0

≈0≈0Ouellet & Bogorad (arXiv:1809.10709)



An Axion In a Magnetic Field

▸ Modification to Ampere’s law (MQS approximation)

▸ An oscillating axion field creates an “effective current” in the presence of a magnetic field

14

Je↵ = ga��@a

@tB

r⇥B = ga��@a

@tB

B0






14

Je↵ = ga��@a

@tB

r⇥B = ga��@a

@tB

B0

Jeff






14

Je↵ = ga��@a

@tB

r⇥B = ga��@a

@tB

B0

Jeff

Ba

ABRACADABRA


10-16

10-14

10-12

10-10

10-8

10-6

10-10 10-8 10-6 10-4 10-2 100

Axio

n Co

uplin

g |G

Aγγ |

(GeV

-1)

Axion Mass mA (eV)

10-16

10-14

10-12

10-10

10-8

10-6

10-10 10-8 10-6 10-4 10-2 100

LSW(OSQAR)

Helioscopes (CAST)

Haloscopes(ADMX and others)

Tele

scop

es

Horizontal Branch Stars

KSVZ

DFSZ

VMB(PVLAS)

SN 1987A

HESSFermi

Sun

ABRACADABRA

Current State Of Axion Search

16

QCD Axio

nALPs

From the PDG


10-16

10-14

10-12

10-10

10-8

10-6

10-10 10-8 10-6 10-4 10-2 100

Axio

n Co

uplin

g |G

Aγγ |

(GeV

-1)

Axion Mass mA (eV)

10-16

10-14

10-12

10-10

10-8

10-6

10-10 10-8 10-6 10-4 10-2 100

LSW(OSQAR)

Helioscopes (CAST)

Haloscopes(ADMX and others)

Tele

scop

es

Horizontal Branch Stars

KSVZ

DFSZ

VMB(PVLAS)

SN 1987A

HESSFermi

Sun

ABRACADABRA

Current State Of Axion Search

16

ABRACADABRA

QCD Axio

nALPs

From the PDG


ABRACADABRA

A New Way to Search for Axion Dark Matter

17

Broadband and Resonant Approaches to Axion Dark Matter Detection

Yonatan Kahn,1,* Benjamin R. Safdi,2,† and Jesse Thaler2,‡1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA(Received 3 March 2016; published 30 September 2016)

When ultralight axion dark matter encounters a static magnetic field, it sources an effective electriccurrent that follows the magnetic field lines and oscillates at the axion Compton frequency. We propose anew experiment to detect this axion effective current. In the presence of axion dark matter, a large toroidalmagnet will act like an oscillating current ring, whose induced magnetic flux can be measured by anexternal pickup loop inductively coupled to a SQUID magnetometer. We consider both resonant andbroadband readout circuits and show that a broadband approach has advantages at small axion masses. Weestimate the reach of this design, taking into account the irreducible sources of noise, and demonstratepotential sensitivity to axionlike dark matter with masses in the range of 10−14-10−6 eV. In particular, boththe broadband and resonant strategies can probe the QCD axion with a GUT-scale decay constant.

DOI: 10.1103/PhysRevLett.117.141801

A broad class of well-motivated dark matter (DM)models consists of light pseudoscalar particles a coupledweakly to electromagnetism [1–3]. The most famousexample is the QCD axion [4–7], which was originallyproposed to solve the strong CP problem. More generally,string compactifications often predict a large number ofaxionlike particles (ALPs) [8], with Planck-suppressedcouplings to electric (E) and magnetic (B) fields of theform aE ·B. Unlike QCD axions, generic ALPs do notnecessarily couple to the QCD operatorG ~G, where G is theQCD field strength. The masses and couplings of ALP DMcandidates are relatively unconstrained by theory or experi-ment (see Refs. [9–11] for reviews). It is therefore impor-tant to develop search strategies that cover many orders ofmagnitude in the axion parameter space.The ADMX experiment [12–14] has already placed

stringent constraints on axion DM in a narrow mass rangearound ma ∼ few × 10−6 eV. However, ADMX is onlysensitive to axion DM whose Compton wavelength iscomparable to the size of the resonant cavity. For theQCD axion, the axion mass ma is related to the Peccei-Quinn (PQ) symmetry-breaking scale fa via

fama ≃ fπmπ; ð1Þ

where mπ ≈ 140 MeV (fπ ≈ 92 MeV) is the pion mass(decay constant). Lighter QCD axion masses thereforecorrespond to higher-scale axion decay constants fa. TheGUT scale (fa ∼ 1016 GeV, ma ∼ 10−9 eV) is particularlywell motivated, but well beyond the reach of ADMX assuch small ma would require much larger cavities. Moregeneral ALPs can also have lighter masses and largercouplings than in the QCD case.In this Letter, we propose a new experimental design

for axion DM detection that targets the mass rangema ∈ ½10−14; 10−6$ eV. Like ADMX, this design exploits

the fact that axion DM, in the presence of a static magneticfield, produces response electromagnetic fields that oscillateat the axion Compton frequency. Whereas ADMX is basedon resonant detection of a cavity excitation, our design isbased on either broadband or resonant detection of anoscillating magnetic flux with sensitive magnetometers,sourced by an axion effective current. Our static magneticfield is generated by a superconducting toroid, which has theadvantage that the flux readout system can be external tothe toroid, in a region of ideally zero static field. Crucially,this setup can probe axions whose Compton wavelength ismuch larger than the size of the toroid. If this experimentwere built, we propose the acronym ABRACADABRA, for“A Broadband or Resonant Approach to Cosmic AxionDetection with an Amplifying B -field Ring Apparatus.”For ultralight (sub-eV) axion DM, it is appropriate to

treat a as a coherent classical field, since large DM numberdensities imply macroscopic occupation numbers for eachquantum state. Solving the classical equation of motionwith zero DM velocity yields

aðtÞ ¼ a0 sinðmatÞ ¼ffiffiffiffiffiffiffiffiffiffiffi2ρDM

p

masinðmatÞ; ð2Þ

where ρDM ≈ 0.3 GeV=cm3 is the local DM density [15].(The local virial DM velocity v ∼ 10−3 will give smallspatial gradients ∇a ∝ v.) Through the coupling to theQED field strength F μν,

L ⊃ −1

4gaγγaF μν

~F μν; ð3Þ

a generic axion will modify Maxwell’s equations [16], andAmpère’s circuit law becomes

∇ ×B ¼ ∂E∂t − gaγγ

"E ×∇a −B

∂a∂t

#; ð4Þ

PRL 117, 141801 (2016) P HY S I CA L R EV I EW LE T T ER Sweek ending

30 SEPTEMBER 2016

0031-9007=16=117(14)=141801(6) 141801-1 © 2016 American Physical Society


ABRACADABRA

A Broadband/Resonant Approach to Cosmic Axion Detection with an Amplifying B-Field Ring Apparatus

▸ Start with a toroidal magnet with a fixed magnetic field B0

18

B0

Rin

Rout

h

Phys. Rev. Lett. 117, 141801 (2016)


ABRACADABRA



▸ ADM generates an oscillating effective current around the ring (MQS approx: λ≫R)

18

B0

Rin

Rout

h

Jeff

Phys. Rev. Lett. 117, 141801 (2016)


ABRACADABRA




▸ … this generates an oscillating magnetic field through the center of the toroid

18

B0

Rin

Rout

h

Jeff

Ba

Phys. Rev. Lett. 117, 141801 (2016)


ABRACADABRA





▸ Insert a pickup loop in the center and measure the induced current in the loop read out by a SQUID based readout

18

B0

Rin

Rout

h

Jeff

Ba

r

�(t) = ga��Bmax

p2⇢DM cos(mat)GV V

Phys. Rev. Lett. 117, 141801 (2016)


ABRACADABRA





▸ Insert a pickup loop in the center and measure the induced current in the loop read out by a SQUID based readout

18

B0

Rin

Rout

h

Jeff

Ba

r

No axions = No B-field

�(t) = ga��Bmax

p2⇢DM cos(mat)GV V

Phys. Rev. Lett. 117, 141801 (2016)


ABRACADABRA

ABRACADABRA on the Back of the Envelope

▸ Rin = 1m, Rout = 2m, h=3m

▸ Bmax = 5T

▸ ma = 1 neV, KSVZ

19

B0

Rin

Rout

h

r

QCD axion


ABRACADABRA



▸ Bmax = 5T


➡ Ba~5×10-22 T

19

B0

Rin

Rout

h

r

QCD axion


ABRACADABRA



▸ Bmax = 5T


➡ Ba~5×10-22 T

19


ABRACADABRA



▸ Bmax = 5T


➡ Ba~5×10-22 T

▸ Will require extremely sensitive quantum limited field sensors!

19


ABRACADABRA-10 cm Data

Axions in Power Spectra

▸ Collect continuous time series data and Fourier transform into frequency space

▸ Average over many time periods to beat down the noise

20

�f

f0⇠ 10�6

Doppler Broadening from DM velocity



Axions in Power Spectra

▸ Collect continuous time series data and Fourier transform into frequency space

▸ Average over many time periods to beat down the noise

▸ Highest useful frequency set by Nyquist frequency

▸ Lowest useful frequency set by ability to resolve the axion line (equal to 1/buffer time)

20

�f

f0⇠ 10�6

Doppler Broadening from DM velocity


ABRACADABRA

Two Readout Approaches

21

f = ma/2⇡

�f ⇡ 1/�v2a ⇠ 10�6

Noise Floor

‣ Option A: Measure and Average ‣ Can search all frequencies simultaneously ‣ Averaging is really slow

�(t) = ga��p

2⇢DMV GV Bmax cos(mat) + n(t)

ga��p

2⇢DMV GV Bmax ⌧ |n|


ABRACADABRA

Two Readout Approaches

21

f = ma/2⇡

�f ⇡ 1/�v2a ⇠ 10�6

Noise Floor

‣ Option A: Measure and Average ‣ Can search all frequencies simultaneously ‣ Averaging is really slow

‣ Option B: Lock in and amplify one frequency ‣ Can quickly pull signal from noise ‣ Don’t know what frequency to amplify!

�(t) = ga��p

2⇢DMV GV Bmax cos(mat) + n(t)

ga��p

2⇢DMV GV Bmax ⌧ |n|

�f

f0⇠ 10�6


ABRACADABRA

ABRACADABRA Broadband Readout

▸ ABRACADABRA will require very sensitive current detectors → SQUID current sensors

▸ The pickup loop is coupled directly into the SQUID input and all frequencies are acquired equally

▸ Able to search all frequencies simultaneously

▸ The noise floor is set by the flux noise in the SQUID

22

3

LpLi

L

M

LLpLi

M

CR

Δω

Figure 3. Schematics of our readout circuits. Left: broad-band (untuned magnetometer). The pickup loop Lp is placedin the toroid hole as in Fig. 1 and connected in series withan input coil Li, which has mutual inductance M with theSQUID of self-inductance L. Right: resonant (tuned mag-netometer). Lp is now in series with both Li and a tun-able capacitor C. A “black box” feedback circuit modulatesthe bandwidth �! and has mutual inductance M with theSQUID.

loop of radius r R can be written as

�pickup(t) = ga�� Bmax

p2⇢DM cos(mat)VB . (7)

The e↵ective volume containing the external B-field is

VB =

Z r

0dr0

Z R+a

Rds

Z 2⇡

0d✓

Rhr0(s� r0 cos ✓)

r2ph2 + 4r2

, (8)

with r2 ⌘ s2 + r02 � 2sr0 cos ✓. We work in the magneto-quasistatic limit, 2⇡/ma � r,R, h, a; at higher frequen-cies, displacement currents can potentially screen our sig-nal. As an illustration, we consider a meter-sized exper-iment, where VB = 1 m3 for r = R = a = h/3 = 0.85m, with sensitivity to ma

<⇠ 10�6 eV. For an example of

the magnitude of the generated fields, the average B-fieldsourced by a GUT-scale KSVZ axion (fa = 1016 GeV)with VB = 100 m3 and Bmax = 5 T is 2.5⇥ 10�23 T. Todetect such a small B-field at this frequency, we need aflux noise sensitivity of 1.2⇥ 10�19 Wb/

pHz for a mea-

surement time of 1 year in a broadband strategy (seebelow). The anticipated reach for various VB and Bmax

is summarized in Fig. 2.Broadband approach—In an untuned magnetometer, a

change in flux through the superconducting pickup loopinduces a supercurrent in the loop. As shown in Fig. 3(left), the pickup loop (inductance Lp) is connected inseries with an input coil Li, which is inductively coupledto the SQUID (inductance L) with mutual inductanceM .The flux through the SQUID is proportional to the fluxthrough the pickup loop and is maximized when Li ⇡

Lp [41]:

�SQUID ⇡↵

2

sL

Lp�pickup. (9)

Here ↵ is an O(1) number, with ↵2⇡ 0.5 in typical

SQUID geometries [42].Clearly, the flux through the SQUID will be maximized

for L as large as possible and Lp as small as possible. A

typical SQUID has inductance L = 1 nH. A supercon-ducting pickup loop of wire radius � = 1 mm and loopradius r = 0.85 m has geometric inductance of [43]

Lp = r(ln(8r/�)� 2) ⇡ 7 µH, (10)

but this may be reduced with smaller loops in parallel asin a fractional-turn magnetometer [44, 45].2 The mini-mum inductance is limited by the magnetic field energy12

RB2 dV stored in the axion-sourced response field, and

is approximately

Lmin ⇡ ⇡R2/h. (11)

With a “tall” toroid where h = 3R, one can achieveLmin ⇡ 1 µH and �SQUID ⇡ 0.01�pickup for R = 0.85m. Since the pickup loop area is much larger than themagnetometer area, the B-field felt by the SQUID is sig-nificantly enhanced compared to the axion-induced fieldin the pickup loop. The B-field enhancement takes ad-vantage of the fact that we are working in the near-fieldlimit, so that the induced B-field adds coherently overthe pickup loop.To assess the sensitivity of the untuned magnetome-

ter to the axion-sourced oscillating flux in (7), we mustcharacterize the noise of the circuit. In a pure supercon-ducting circuit at low frequencies, there is zero noise inthe pickup loop and input coil, and the only source ofnoise is in the SQUID, with contributions from thermalfluctuations of both voltage and current. Despite theirthermal origin, we will refer to these as “magnetome-ter noise” to distinguish them from noise in the pickuploop circuit (which dominates in the resonant case be-low). At cryogenic temperatures (T <

⇠ 60 mK), thermalcurrent and voltage noise are subdominant to the cur-rent shot noise SJ,0 in the SQUID tunnel junctions [42],which sets an absolute (temperature-independent) floorfor the magnetometer noise. See the appendix for a moredetailed discussion of noise in a real implementation ofthis design.A typical, temperature-independent flux noise for com-

mercial SQUIDs at frequencies greater than ⇠10 Hz is

S1/2�,0 ⇠ 10�6�0/

p

Hz, (12)

where �0 = h/(2e) = 2.1⇥10�15 Wb is the flux quantum.We use this noise level and a fiducial temperature of 0.1K as our benchmark. DC SQUIDS are also known toexhibit 1/f noise which dominates below about 50 Hzat 0.1 K [46]. We estimate the reach of our broadbandstrategy down to 1 Hz assuming 1/f noise is the soleirreducible source of noise at these low frequencies, but in

2 We thank Chris Tully and Mike Romalis for suggesting this strat-egy to us.

Pickup Loop SQUID


ABRACADABRA

ABRACADABRA Resonant Readout

▸ Insert a resonator into the circuit that resonantly enhances the signal before the SQUID noise is introduced

▸ Resonator is charged when driven on resonance by the axion field

▸ Pickup loop acts as a weak coupling between axion field and resonator

▸ Power flowing into our resonator is tiny, so power flowing out should be comparably small

➡ High Q resonator

➡ The need to scan (and scan quickly)

23

Axion Field Resonator

Pickup Loop

3

LpLi

L

M

LLpLi

M

CR

Δω






VB =

Z r

0dr0

Z R+a

Rds

Z 2⇡

0d✓


r2ph2 + 4r2

, (8)




pHz for a mea-




Lp [41]:

�SQUID ⇡↵

2

sL

Lp�pickup. (9)





Lp = r(ln(8r/�)� 2) ⇡ 7 µH, (10)



is approximately

Lmin ⇡ ⇡R2/h. (11)





S1/2�,0 ⇠ 10�6�0/

p

Hz, (12)



Pickup Loop SQUID

Resonator

ABRACADABRA-10CM

A PROTOTYPE DETECTOR


ABRACADABRA-10 cm

Dissecting ABRACADABRA-10 cm

25


ABRACADABRA-10 cm


25

12 cm

12 c

m

B0 = 1T


ABRACADABRA-10 cm


25


ABRACADABRA-10 cm


25

Superconducting Pickup Loop

rp = 2 cm

Superconducting Calibration Loop

rc = 4.5 cm

Delrin Toroid Body

80×16 NbTi (CuNi) winds (counter-wound)


ABRACADABRA-10 cm


26

G10 Support structure (nylon bolts)

Copper Thermalization Bands

Superconducting tin coated copper shield


ABRACADABRA-10 cm

Assembling ABRACADABRA-10 cm

27

(Normally make MRI magnets!)

SUPERCONDUCTING SYSTEMS INC.

Job Position Available

Superconducting Systems Inc. (SSI) designs and manufactures superconducting magnets for both medical applications and physics research applications. We are seeking a recent graduate with a Master of Science or Bachelor of Science degree in mechanical engineering to participate in the development of innovative magnets for human MRI applications. The candidate should:

1) Have a M.S. or B.S. degree in Mechanical Engineering

2) Be fluent in the Chinese Mandarin language

3) Have completed advanced courses in structural design and analysis

4) Have participated in practical design projects

5) Be skilled with SolidWorks software

6) Be willing to travel

The position is located at Billerica, MA. SSI offers competitive salary and benefits. Work experience of 2-5 years is desirable.

Please contact Francesca Minervini at the below email address with your resume (.pdf form if possible) attached.

Francesca Minervini

Project Engineer/ Mechanical Engineer

[email protected]


ABRACADABRA-10 cm

Assembling ABRACADABRA-10 cm

28


ABRACADABRA-10 cm

ABRA Mounted In Olaf

29

Kevlar Support

700 mK

150 mK


ABRACADABRA-10 cm

SQUID Readouts

▸ Off the shelf Magnicon DC SQUIDs

▸ Typical noise floor ~1 μΦ0/(Hz)1/2

▸ Optimized for operation < 1 K

▸ Typical gain of ~1.3 V/Φ0S (volts per SQUID flux quanta)

▸ No resonator (i.e. broadband readout)

30

SQUID Amplifier Array

Mu Metal Shielding

George Washington

�0 = 2⇥ 10�15 Wb

Quick note on units:We measure magnetic flux in

units of micro flux quanta (μΦ0)


ABRACADABRA-10 cm

Suspension System

31

40 K

2.5 K

800 mK

300 mK

100 mK

300 K

ABRA-10 CM


ABRACADABRA-10 cm

Suspension System

31

40 K

2.5 K

800 mK

300 mK

100 mK

300 K

ABRA-10 CM

Accelerometer on the 300K plate


ABRACADABRA-10 cm

Suspension System

31

40 K

2.5 K

800 mK

300 mK

100 mK

300 K

ABRA-10 CM

Flux through the ABRA pickup loop

Accelerometer on the 300K plate


ABRACADABRA-10 cm

Magnetic Shielding

▸ Two layers of mu-metal shielding

▸ Recycled from the Bates Accelerator Pipe

▸ DC Attenuation ~ 10x

32

ABRA

COMMISSIONING AND DATA TAKING

ABRACADABRA-10 CM



Vibrational Noise (Magnet On)

▸ Huge amount of noise below ~10 kHz, strongly correlated with vibration on the 300K plate

▸ Had to use a 10kHz high pass filter to get the data to fit in the digitizer window

▸ Hard limit on the low end search window

34

*Accelerometer loses sensitivity above a few

kHz

ABRACADABRA-10 cm Preliminary




Calibration

▸ Perform calibration by injecting current into the calibration loop measuring the spectrum

▸ Fine scan from 10 kHz - 3 MHz at multiple amplitudes

▸ Requires a total of ~90 dB of attenuation to get “reasonable” size signals

▸ Gain lower than expected by a factor of ~6.5 (suspect parasitic inductance)

35




Broadband Data Collection Procedure▸ Collected data with magnet on continuously for 4 weeks from July - August

▸ Sampling at 10 MS/s for 2.4 × 106 seconds (25T samples total)

▸ Digitizer locked to a Rb oscillator frequency standard

▸ Acquisition (currently) limited to 1 cpu and 8 TB max data size

36

10 MS/s Sampling 1 MS/s Sampling 100 kS/s Sampling

Average PSDs of 10 s waveforms

Written to disk every 800 seconds

∆f = 100 mHz

Average PSDs of 100 s waveforms

Written to disk every 1600 seconds

∆f = 10 mHz

Written directly to disk

2,452,000 seconds total

∆f ≈ 408 nHz



Example Spectrum

▸ Filter SQUID output through 10 kHz high-pass and 1.9MHz anti-aliasing filter

▸ Digitizer noise (taken in dedicated run) shows spurious noise spikes that were vetoed.

37

~9 hours of data

ma ~ neV (GUT scale PQ)




Transient Noise at High Frequency

▸ Appeared after we were in the lab

▸ Seemed to be correlated with working hours? ▸ Investigating the digitizer/DAQ computer, grounding schemes, shielding,

etc… ▸ In the present analysis, we had to discard ~30% of the data

38





Magnet Off Data

▸ Collected 2 weeks of magnet off data with the same configuration

▸ High frequency transient noise also present

▸ Significantly lower noise background around 10kHz (vibration of stray fields)

▸ Used for spurious signal veto

39

Averaged over ~9




ABRACADABRA-10 cm First Dataset

40

10 MS/s Dataset 1 MS/s Dataset

Integrated Time

471 h 427h

Individual Spectra

2120 960

Frequency Range

500 kHz - 3 MHz 75 kHz - 500 kHz


AXION SEARCHABRACADABRA-10 CM


ABRACADABRA Axion Search

Axion Signal

▸ Time averaged flux through the pickup loop:

▸ Signal shape given by the standard halo model

42

h�2Pickupi = g2a��⇢DMV 2G2B2

max ⌘ A (Units: µ�20/Hz)

Velocity distribution of DM in the halo

Integral = A



Axion Search Approach

▸ Rebin the data into 53 (24) of our 10 MS/s (1 MS/s) spectra that span the data taking period

▸ Limit our search range to 75 kHz - 2 MHz (ma in 0.31 — 8.1 neV)

▸ For each mass point, we calculate a likelihood function

▸ Power bins are Erlang distributed with shape parameter Navg (average over Navg exponential distributions) and mean si,k+bi

▸ Depends only on gaγγ and nuisance parameters, bi, which are assumed to be constant across the axion signal, but can vary slowly in time

43

L =

NSpectraY

i

NFreqY

j

Erlang(NAvg, si,k + bi)



Axion Search Approach

▸ We then perform our axion discovery search based on a log-likelihood ratio test, between the best fit and the null hypothesis

▸ Profiling over all nuisance parameters, bi

▸ We set the 5σ discovery threshold as TS>56.1 (accounting for the Look Elsewhere Effect for our 8M mass points)

44

TS = 2hlogL

⇣ga�� ,ma, b

⌘� logL

⇣ga�� = 0,ma,

ˆb⌘i

ABRACA




Axion Limits

▸ We saw no 5σ excesses that were not vetoed by Magnet off or digitizer data

▸ 87 (0) mass points were vetoed in the 10MS/s (1MS/s) data

▸ We place 95% C.L. upper limits using a similar log-likelihood ratio approach

▸ Our limits are approaching the limits set by CAST

45





ABRACADABRA-10 cm Run 1 Limits

46

NEXT STEPS


ABRACADABRA Next Generation

ABRACADABRA-75 cm

▸ Goal: Probing the QCD scale axion around the GUT scale (ma ~ neV)

‣ A meter scale detector with a max field of B0~1-5 T

‣ Resonator readout with accelerated* scan readout strategy

‣ Quantum limited sensors able to push beyond the Standard Quantum Limit

‣ Operating at or below 100 mK

‣ We have already begun putting together an interest group and a TDR to follow

48

3m

2.25

m

*Ask more about this!


Summary

Summary

▸ We have built and operated the first broadband search for Axion Dark Matter in the sub μeV range.

▸ With a 10 cm scale detector and 1 month of exposure, we are competitive with the leading limits in the field!

▸ ABRA-10 cm will transition to a test bench for a future more sensitive detector

▸ Putting together a proposal for a ~1 m scale experiment (ABRACADABRA-75 cm)

49



First Results from ABRACADABRA-10 cm: A Search for Sub-µeVAxion Dark Matter

Jonathan L. Ouellet,1, ⇤ Chiara P. Salemi,1 Joshua W. Foster,2 Reyco Henning,3, 4 Zachary Bogorad,1

Janet M. Conrad,1 Joseph A. Formaggio,1 Yonatan Kahn,5, 6 Joe Minervini,7 Alexey Radovinsky,7

Nicholas L. Rodd,8, 9 Benjamin R. Safdi,2 Jesse Thaler,10 Daniel Winklehner,1 and Lindley Winslow1, †

1Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.

2Leinweber Center for Theoretical Physics, Department of Physics,

University of Michigan, Ann Arbor, MI 48109, U.S.A.3University of North Carolina, Chapel Hill, NC 27599, U.S.A.

4Triangle Universities Nuclear Laboratory, Durham, NC 27708, U.S.A.

5Princeton University, Princeton, NJ 08544, U.S.A.

6Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, U.S.A.

7Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.

8Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, U.S.A.

9Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.

10Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.

(Dated: October 29, 2018)

The axion is a promising dark matter candidate, which was originally proposed to solve the strong-CP problem in particle physics. To date, the available parameter space for axion and axion-likeparticle dark matter is relatively unexplored, particularly at masses ma . 1µeV. ABRACADABRAis a new experimental program to search for axion dark matter over a broad range of masses,10�12 . ma . 10�6 eV. ABRACADABRA-10 cm is a small-scale prototype for a future detectorthat could be sensitive to the QCD axion. In this Letter, we present the first results from a 1monthsearch for axions with ABRACADABRA-10 cm. We find no evidence for axion-like cosmic dark mat-ter and set 95% C.L. upper limits on the axion-photon coupling between ga�� < 1.4⇥ 10�10 GeV�1

and ga�� < 3.3⇥ 10�9 GeV�1 over the mass range 3.1⇥ 10�10 eV – 8.3⇥ 10�9 eV. These results arecompetitive with the most stringent astrophysical constraints in this mass range.

INTRODUCTION

The particle nature of dark matter (DM) in the Uni-verse remains one of the greatest mysteries of contempo-rary physics. Axions are an especially promising candi-date as they can simultaneously explain both the parti-cle nature of DM and resolve the strong-CP problem ofquantum chromodynamics (QCD) [1–6]. Axion-like par-ticles (ALPs) are generically expected to have a couplingto electromagnetism of the form [7]

L � �1

4ga��a eFµ⌫F

µ⌫ = ga��aE ·B, (1)

where ga�� is the axion-photon coupling. The QCD axionis predicted to have a narrow range of couplings propor-tional to the axion mass, while a general ALP may haveany ga�� . In this work, “axion” refers to a general ALP.Axion DM (ADM) with mass ma ⌧ 1 eV behaves todayas a classical field oscillating at a frequency f = ma/(2⇡)[3, 4]. The Lagrangian (1) implies that a time-dependentbackground density of ADM modifies Maxwell’s equa-tions. In particular, in the presence of a static magneticfield B0, ADM generates an oscillating magnetic field,Ba, as if sourced by an e↵ective AC current density par-allel to B0 [8],

Je↵ = ga��p

2⇢DMB0 cos(mat). (2)

Here ⇢DM is the local DM density, whichwe take to be 0.4GeV/cm3 [9, 10]. The ABroadband/Resonant Approach to Cosmic AxionDetection with an Amplifying B-field RingApparatus (ABRACADABRA) experiment, as firstproposed in [11], is designed to search for the axion-induced field, Ba, generated by a toroidal magnetic field(see also [12] for a proposal using a solenoidal field).ABRACADABRA searches for an AC magnetic fluxthrough a superconducting pickup loop in the center ofa toroidal magnet, which should host no AC flux in theabsence of ADM. The time-averaged magnitude of theflux through the pickup loop due to Ba can be writtenas

|�a|2 = g2a��⇢DMV 2G2B2max ⌘ A, (3)

where V is the volume of the toroid, G is a geometric fac-tor calculated for our toroid to be 0.027 [13], and Bmax

is the maximum B-field in the toroid. The pickup loopis read out using a SQUID current sensor, where an ax-ion signal would appear as a small-amplitude, narrow(�f/f ⇠ 10�6) peak in the power spectral density (PSD)of the SQUID output at a frequency given by the axionmass. The present design uses a simplified broadbandreadout, but the same approach can be significantly en-hanced using resonant amplification and recent develop-ments in powerful quantum sensors [14, 15], which is thesubject of future work.

Summary

On the arXiv!

50

ARXIV:1810.12257


Summary

We’ve Explained the Acronym!

51

A B R A C A D A B R A

3

LpLi

L

M

LLpLi

M

CR

Δω






VB =

Z r

0dr0

Z R+a

Rds

Z 2⇡

0d✓


r2ph2 + 4r2

, (8)




pHz for a mea-




Lp [41]:

�SQUID ⇡↵

2

sL

Lp�pickup. (9)





Lp = r(ln(8r/�)� 2) ⇡ 7 µH, (10)



is approximately

Lmin ⇡ ⇡R2/h. (11)





S1/2�,0 ⇠ 10�6�0/

p

Hz, (12)



Pickup Loop SQUIDAxion Field Resonator

Pickup Loop

A Broadband/Resonant Approach

Amplifying B-Field Ring Apparatus

Cosmic Axion Detection

Je↵ = ga��@a

@tB


ABRACADABRA Collaboration

ABRACADABRA

52

Thank you for your attention!

a broadband/resonant search for axion dark...

Documents